Question
Download Solution PDFयदि X और Y दो यादृच्छिक चर हैं, जिनका घनत्व फलन
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसही विकल्प 2 है।
विस्तृत हल:
अवधारणा:
दो यादृच्छिक चर X और Y के संयुक्त संचयी फलन को इस प्रकार परिभाषित किया जाता है:
संयुक्त CDF निम्नलिखित गुणों को संतुष्ट करता है:
, किसी भी y के लिए (Y का सीमांत CDF)
, किसी भी x के लिए (X का सीमांत CDF) - P(x1 < X < x2, y1 < Y < y2) = FXY(x2, y2) - FXY(x1, y2) - FXY(x2, y1) + FXY(x1, y1)
- यदि X और Y स्वतंत्र हैं, तो FXY(x, y) = FXY(x) FXY(y)
दो यादृच्छिक चर X और Y संयुक्त रूप से सतत हैं, यदि एक गैर-ऋणात्मक फलन fXY : ℝ2 → ℝ का अस्तित्व इस प्रकार है कि किसी भी समुच्चय A ∈ ℝ2 के लिए, हमें प्राप्त है:
गणना:
Last updated on Jul 8, 2025
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